Humber Polytechnic · CALC 103

Humber Polytechnic CALC 103 tutoring

Help with limits, derivatives, basic integrals and technical applications.

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Course overview

CALC 103 covers limits, derivatives and basic integrals with technical applications, including motion, area, current and charge. Humber’s published mathematics requirements list it in engineering technician and technology diploma pathways. In the example below, you’ll use integration to distinguish net charge transfer from the total amount of charge that moves.

The topics here come from the 2025–26 course description. We have not confirmed their alignment with the 2026–27 outline. Your current outline, if you have it, helps us identify the topics you’re studying.

CALC 103 topics to review

Limits, derivatives, curve sketching and optimizationBasic algebraic, trigonometric, logarithmic and exponential integralsParticle motion, area and net changeCircuit current and charge applications

Common difficulties

Treating zero net change as no activity
Ignoring a sign change when calculating an unsigned total

Useful foundations to review

Review powers, factoring, function graphs and the units attached to rates. Practise differentiating a proposed antiderivative before evaluating its bounds. On a signed-rate graph, mark every zero inside the interval so opposite contributions remain visible.

Registration requirements

The guidance above is study preparation, not an eligibility decision. Confirm current prerequisites, restrictions and availability with Humber Polytechnic.

Check the official course catalogue

Separate net charge from total charge movement

A signed current is $i(t)=3t^2-6t$ amperes for $0\leq t\leq3$ seconds. Find the net charge transferred and the total magnitude of charge passing the reference point.

Show the reasoning

Locate the reversal
Factor $i(t)=3t(t-2)$ . The current is negative between 0 and 2 seconds and positive between 2 and 3 seconds. Negative current means flow opposite the chosen reference direction.
Calculate the net transfer
An antiderivative is $F(t)=t^3-3t^2$ . Thus $\Delta Q=F(3)-F(0)=0\text{ C}$ . Since amperes are coulombs per second, integration over seconds gives coulombs.
Add magnitudes on separate intervals
The signed transfers are $F(2)-F(0)=-4\text{ C}$ and $F(3)-F(2)=4\text{ C}$ . Their magnitudes total $8\text{ C}$ . Zero net transfer does not mean no charge passed.

Try an independent variation

For a new current $i(t)=2t-4$ A on $0\leq t\leq5$ s, find both quantities.

Check your reasoning

The reversal is at 2 s. With $F(t)=t^2-4t$ , the signed transfers are −4 C and 9 C. Net charge is $5\text{ C}$ ; total magnitude is $13\text{ C}$ .

How tutoring can help

You can bring a problem even if you’re unsure how to begin. A tutor can help identify the quantity being asked for, read the rate graph and build the integral step by step. If you’ve already tried it, you can review the calculation together, understand any sign errors and practise a similar example.

Exam preparation for CALC 103

Alternate derivative questions with basic integral applications from your announced chapters. Label each result with its physical meaning and unit. When the rate changes sign, predict whether cancellation is possible before integrating, then check your antiderivative by differentiation.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Independent practice

Free practice and study guides for CALC 103

10 min

Derivative Rules: Choose the First Step

Choose the first derivative rule in three core questions, then explore an optional logarithmic-differentiation example and retry when both base and exponent vary.

35 min

How to Choose an Integration Method

Compare substitution, integration by parts, partial fractions and trigonometric substitution, with sign-aware radical choices, worked examples and progressive checks.

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CALC 103 · official course reference